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Helmholtz

Benchmarks

Task NameDataset NameSOTA ResultTrend
Physics-Informed PDE Solving2D Helmholtz (test)
Time (sec/iter)0.0228
14
Inverse PDE solvingHelmholtz full observations
Relative Error0.049
14
Spatio-temporal PDE reconstructionHelmholtz
PDE Residual0.55
12
PDE ReconstructionHelmholtz 3% uniformly random measurements
Coefficient Relative L2 Error7.67
10
Forward PDE solvingHelmholtz Full Observation
L2 Relative Error0.0108
9
Forward PDE SolvingHelmholtz (test)
Relative H1 Error0.233
9
Inverse problemHelmholtz
PDE Residual0.2
9
Forward PDE solvingHelmholtz
PDE Residual0.37
9
PDE Inverse ProblemHelmholtz Noisy
L2 Relative Error67.93
7
PDE Forward ProblemHelmholtz Noisy
L2 Relative Error16.84
7
Conditional source inferenceHelmholtz 256 samples (test)
Relative L2 Error0.381
6
Operator Learning for PDEsHelmholtz (downstream)
EG Score78.3
6
InverseHelmholtz 30% noise corruption 1.0 (test)
L2 Relative Error0.5443
5
ForwardHelmholtz 30% noise corruption 1.0 (test)
L2 Relative Error9.16
5
Inverse PDE SolvingHelmholtz 10% noise corruption
L2 Relative Error43.56
5
Forward PDE SolvingHelmholtz 10% noise corruption
L2 Relative Error8.05
5
InverseHelmholtz 50% pixels noise
L2 Relative Error0.5999
5
ForwardHelmholtz 50% pixels noise
L2 Relative Error12.04
5
InverseHelmholtz 90% pixels corrupted by noise
L2 Relative Error66.93
5
ForwardHelmholtz 90% pixels corrupted by noise
L2 Relative Error16.16
5
Inverse ProblemHelmholtz (test)
RE1.64
5
Forward ProblemHelmholtz (test)
RE2.46
5
Inverse PDE solvingHelmholtz
Relative Error22.6
5
Forward PDE solvingHelmholtz full observations
Relative Error0.023
5
PDE SolvingHelmholtz (test)
Relative L2 Error0
3
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